Phenomenological Relaxation Time Research Articles

Spin accumulation without spin current

The spin Hall (SH) effect is a phenomenon in which the spin current flows perpendicular to an applied electric field and causes the spin accumulation at the boundaries. However, in the presence of spin-orbit couplings, the spin current is not well defined. Here, we calculate the spin response to an electric field gradient, which naturally appears at the boundaries. We derive a generic formula using the Bloch wave functions and the phenomenological relaxation time. We also calculate the response for the Rashba model with $\delta$-function nonmagnetic disorder within the first-order Born approximation and corresponding vertex corrections. We find the nonzero spin accumulation, although the SH conductivity exactly vanishes.

Tunable, omnidirectional, and nearly perfect resonant absorptions by a graphene-hBN-based hole array metamaterial.

In this paper, we propose an electrically tunable mid-infrared plasmonic-phononic absorber with omnidirectional and polarization insensitive nearly perfect resonant absorption characteristics. The absorber consists of a graphene/hexagonal boron nitride (hBN)/graphene multilayer on top of a gold bottom reflector separated by a dielectric spacer. The graphene/hBN/graphene multilayer is patterned as a hole array in square lattice. We analytically and numerically prove that, due to the support of hybrid plasmon-phonon-polaritons, nearly perfect multi-resonant absorption peaks with high quality factors are obtained both inside and outside of the Reststrahlen band of hBN. As a result of the hybridization of graphene plasmons with the hyperbolic phonon polaritons of hBN, the high quality resonant absorptions of the metamaterial are almost unaffected by decreasing the phenomenological electron relaxation time of graphene. Moreover, the obtained resonances can be effectively tuned in practice due to the continuity of the graphene layers in the hole array metamaterial. These features make the graphene-hBN metamaterial a skeptical design for practical purposes and mid-infrared multi-functional operations such as sensing.

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.

Using relaxation time approximation for collisions in laser-cluster interaction simulation

Numerical experiments were performed for cluster dynamics on a one-dimensional cluster model consisting of hydrogen atoms exposed to intense laser pulses. The algorithm deployed the relativistic equations for solving motions of both protons and electrons, respectively. In contrary to traditionally and extensively used method which treats collisions within a jumbo cluster in a statistical way, we introduced a phenomenological relaxation time parameter to cope collisions among particles in a cluster, thereby profoundly reducing computational workload while still attaining the essential physics. Positive ion’s maximum kinetic energy and maximum kinetic energy saturation with laser intensity were explored, which were found to be in fairly good accordance with experimental observations, corroborating the effectiveness of our method and inferring that this treatment is useful in numerical experiments on light-cluster interaction.

Phase Space Prediction of Product Branching Ratios: Canonical Competitive Nonstatistical Model

We present a new model for predicting branching ratios of chemical reactions when a branching of the reaction path occurs after the dynamical bottleneck, including the case where it occurs after an intermediate. The model is based on combining nonstatistical phase space theory for the direct component of a reaction with variational transition-state theory for an indirect component of reaction. The competition between direct and indirect processes is treated by an extension of the unified statistical model. This new method provides a way to understand the factors that control this kind of chemical reaction and to perform calculations using high-level electronic structure methods for complex systems. The model is based on quantized energy levels of transition states and products, and it involves the same information as required for calculating transition-state rate constants and equilibrium constants plus a phenomenological relaxation time, which was taken from previous work. For the textbook reaction of the hydroboration of propene by BH(3) it has recently been inferred that the selectivity can only be understood by consideration of dynamical trajectories. However, the calculated branching fraction of this prototype reaction increases from 2%-3% when calculated under the inappropriate assumption of complete equilibration of the intermediate to from 8%-9% when calculated with the new theory, which requires only limited information about the system and does not involve running trajectories. The calculated result is in reasonable agreement with experiment (approximately 10%).

Simple method for determining the critical molecular weight from the loss modulus

AbstractThe normal concept is that the critical molecular weight (MC) is about twice as large as the entanglement molecular weight (Me). However, experimental data have shown considerable deviations from MC ≈ 2Me. Furthermore, a determination of MC requires samples with a wide range of molecular weights, including weights lower than MC and higher than MC. In this article, we suggest a simple method for determining MC from the loss moduli of nearly monodisperse linear polymers with M ≫ MC. We consider two characteristic relaxation times, which correspond to the local maximum and minimum of the loss modulus. MC is determined from the intersection of two phenomenological relaxation times as a function of the molecular weight. The method precisely agrees with MC ≈ 2Me, which is not shown by conventional methods. Moreover, our method provides a determination of relaxation time τe, at which chain segments first feel the constraints imposed by the conceptual tube, without the measurement of the tube diameter and the monomeric friction coefficient, which may be determined by complicated procedures with a lot of data. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2724–2729, 2004

Shot noise in resonant-tunneling structures

We propose a quantum-mechanical approach to noise in resonant-tunneling structures that can be applied in the whole range of transport regimes, from completely coherent to completely incoherent. In both limiting cases, well-known results which have appeared in the literature are recovered. Shot noise reduction due to both Pauli exclusion and Coulomb repulsion, and their combined effect, are studied as a function of the rate of incoherent processes in the well (which are taken into account by means of a phenomenological relaxation time), and of temperature. Our approach allows the study of noise in a variety of operating conditions (i.e., equilibrium, subpeak voltages, second-resonance voltages), and as a function of temperature, explaining experimental results and predicting interesting results, such as the dependence of noise on filled-emitter states and the prediction of both increasing and decreasing shot noise with increasing temperature, depending on the structure. It also allows the determination of the major contributions to shot-noise suppression by performing noise measurements at the second-resonance voltage.

Third-order nonlinear susceptibility of large semiconductor microcrystallites.

We show that the theory of the third-order nonlinear susceptibility of semiconductor microcrystallites with a radius much greater than the exciton radius (``weak confinement'') has big intrinsic uncertainties due to the unknown volume dependence of the phenomenological relaxation times. These dependencies are actually sources of another type of optical nonlinearity. The third-order susceptibility increases strongly with the increasing radius of the microcrystallite in the range between 10 and 100 exciton Bohr radii and approaches a well-defined infinite radius limit.

Electrodynamic and microwave properties of high-temperature superconductors: Model calculations for coupled weak links

We calculate the response of an array of resistively-shunted SNS junctions to a combined d.c. + a.c. magnetic field. At sufficiently low frequencies, the induced magnetization exhibits many higher harmonics. There is strong nonresonant absorption of power which is highly dependent on d.c. magnetic field at low frequencies. A phenomenological relaxation time is introduced to describe temperature-dependent effects.

The effect of a phenomenological relaxation time on the magnetoplasmons in a two-dimensional inhomogeneous electron gas

We investigate the effect of a phenomenological relaxation time on the magnetoplasma excitations of a 2D strip of electrons by using the scheme proposed in a previous paper. Particular attention is put on the lowest frequency mode which exhibits an "anomalous" dependence on the static magnetic field (perpendicular to the strip). We show that also the life time of the first mode has an anomalous dependence on the wavevector parallel to the strip and on the magnetic field.

Zener transitions in dissipative driven systems.

The effect of inelastic interactions on Zener transitions is studied in the context of externally driven systems (flux-driven normal metallic rings, current-biased tunnel junctions, etc.). We employ a time-dependent Hamiltonian and use a two-level approximation to study these systems. We consider a coupling (not necessarily weak) of the system to a phonon bath and allow for a large class of phonon spectra. The coupling tends to reduce the Zener tunneling. The Zener transitions are enhanced at finite temperatures. We also consider the effect of a phenomenological relaxation time \ensuremath{\tau} on the behavior of the system, and express the (nonlinear) resistance R in terms of \ensuremath{\tau} and the other important physical parameters. When the bias goes to zero, R vanishes.

Determination of single-particle relaxation time from light scattering spectra in modulation-doped quantum wells.

We report Raman measurements of the ${k}_{?}$ dependence and temperature dependence of the imaginary part of the dielectric function of the electron gas in modulation-doped GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells. The Raman spectra are well explained by the Lindhard response function, using a phenomenological single-particle relaxation time ${\ensuremath{\tau}}_{\mathrm{SP}}$. We determine the temperature dependence of ${\ensuremath{\tau}}_{\mathrm{SP}}$.

Treatment of two phenomenological components in transverse relaxation of rapidly exchanging [formula omitted] cesium-133 nuclei to calculate correlation times

The transverse relaxation of spin- 7 2 cesium-133 ions when interacting with the Gramicidin channel exhibits a phenomenology of two exponential relaxation processes, the relative magnitudes of which vary with CsCl concentration. When the two phenomenological transverse relaxation times, T′ 2 and T″ 2, are used in the formalism for spin- 3 2 nuclei for calculating correlation times, very reasonable values of the correlation times are obtained as judged by their use in calculating Gramicidin single-channel currents. In particular a comparison with spin- 3 2 rubidium-87 transverse relaxation data and the facts that Rb + and Cs + exhibit very similar binding constants and single-channel currents provide a specific demonstration that, when two relaxation processes are observed for spin- 7 2 cesium-133, the use of the two transverse relaxation times in the spin- case3 2 formalism of Bull, Forsén, and colleagues gives rise to correlation times that quite accurately calculate single-channel currents when interpreted as channel occupancy times.

Are vibrational relaxation times really constant? I. The vibrational relaxation of N 2O

The vibrational relaxation of pure N 2O was studied behind shock waves in the temperature range 450–1750 K using a laser beam deflection technique. It is shown that the phenomenological relaxation time,τ′, is not a time-independent constant. Below 1200 K it increases with time; above 1200 K it decreases with time. The many disparate results in the literature are reconciled in terms of a mechanism whereby the step N 2O(0, 0, 0) → N 2O(0, 1, 0) is rate determining at low temperatures when the ν 3 mode is not involved, and the parallel step N 2O(1, 0, 0) + N 2O(0, 0, 0) → N 2O(0, 2, 0) + N 2O(0, 1, 0) takes over at high temperatures close to equilibrium. Rate constants for these processes are extracted from the limiting far-from equilibrium relaxation time, i.e. from τ′(0), where log pτ′(0) = 11.0 T −1 3 −1.67 (in atm μs), and from the limiting near-equilibrium relaxation time, i.e. from τ′(∞), where log pτ′(∞) = 19.4 T −1 3 −2.46 (in atm μs). The relaxation process was simulated by solving the master equation numerically. All energy levels up to 5930 cm −1 connected by all possible VT and inter- and intra-molecular VV processes were included, subject to the restriction that the energy gap ¦Δϵ¦ 700 cm −1. Microscopic rate coefficients, scaled according to ϵ exp(− C ¦Δϵ¦), were assigned, reducing the problem to one of three parameters: C (for VT processes), C VV (for VV processes) and k 01 10/ k 10, where k 10 is the rate constant for N 2O(0, 1, 0) → N 2O(0, 0, 0) and k 01 10 that for N 2O(0, 0, 0) + N 2O(0, 1, 0) → N 2O(0, 0, 0)+N 2O(0,1,0). Computer simulations of shock-induced and laser-induced relaxation are made. They are interpreted in terms of the three parameters. There was semi-quantitative agreement with our experimental results, which are consistent with values for C = 0.0038 cm at room temperature; C VV = 0.021 → 0.0065 cm, and k 01 10/ k 10 ⩽ 5000 → 12.7 in the range 300 → 1800 K. It was further found that intermolecular VV processes are responsible for the time dependence of τ′, and that the increasing density of states accessible at longer times and at higher temperatures is responsible for the change in mechanism.

A phenomenological analysis of ultrasound near phase transitions

Phenomenological predictions for sound attenuation and velocity anomalies near critical points are presented. General symmetry properties of the linear elastic constants and the general properties of the low- and high-frequency behaviours of linear-response functions are used to develop phenomenological equations, where exponents, relaxation times and amplitudes are introduced as parameters to fit to the experimental data. Novel interpretation formulae, which combine the asymptotic high- and low-frequency limits of complex dynamic elastic constants, are constructed. It is shown that causality requirements give new relations between the amplitudes of ultrasonic attenuation and the velocity in the asymptotic limits of high and low frequency.

SHEAR ELASTICITY AND VISCOSITY IN COLLOIDAL CRYSTALS AND LIQUIDS

We have measured the elastic constants of colloidal crystals using a standing cylindrical resonance technique and the viscosity with a variety of rheometers. The elastic constants are well described by Debye-Huckel theory with a renormalized charge. The crystals melt upon addition of electrolyte and the resulting liquid has a viscosity which is strongly dependent upon the electrostatic interactions between the charged colloids. Extrapolation of the elastic constants into the liquid regime, together with a phenomenological relaxation time, allow us to predict the viscosity of the liquid. We also observe a transition from solid to liquid, shear melting, upon application of sufficiently high stress. This transition is accompanied by an increase in viscosity in going from solid to liquid.

Aliphatic polyesters as models for relaxation processes in crystalline polymers: 4. Dielectric relaxation in oriented specimens

To investigate further the effect of the crystal phase on amorphous-phase relaxation, samples of 6-6, 5–7, and 6–10 polyesters have been oriented by extrusion in the solid-state through a tapered die and the dielectric constant and loss measured both parallel and perpendicular to the extrusion direction. The data have been analysed quantitatively in terms of the Cole—Cole phenomenological equation and relaxation times, width parameters and relaxation strengths determined. For the β (glass—rubber relaxation) the relaxation times are shifted 2–3 orders of magnitude to longer times and the relaxation is broadened slightly compared to the unoriented polymers. There also tends to be reduction of overall parallel and perpendicular relaxation strength for the β process on orientation. The γ processes show little effect of orientation on relaxation time and width and do not show reduction of overall relaxation strength. These observations are consistent with crystal displacement further restricting amorphous-phase longer-range segmental motion (β process) but having little effect on the locallized motions associated with the γ process. Both the γ and β processes show anisotropy in relaxation strength. The anisotropy is analysed with a newly developed theory to separate inherent phase anisotropy from apparent anisotropy due to composite or form effects. The average angle made by the lamellar surface normal to the extrusion direction enters as a parameter in the theory. Measurements of relaxed specimen ε  and ε ⊥ values for both the γ and β processes serve to determine both f a the amorphous-phase orientation function and the average tilt angle for the specimens here. This is possible because for the γ process relaxation strength is small and specimen anisotropy is dominated by inherent phase anisotropy but for the γ + β processes larger relaxation strength leads to specimen anisotropy being strongly influenced by crystal—amorphous phase composite effects. Values of f a are in the range of 0.05–0.20 for specimens with f c in the range 0.5–0.9. Indicated lamellar tilt angles are in the range of 24°–80°.

Optical properties of paramagnetic iron

Using the model interpolation scheme band structure of paramagnetic iron given recently by Baker and Smith (1977) and the special direction method for performing the Brillouin zone integrations the authors report calculations of the imaginary part of the dielectric function and optical conductivity. The effect of including matrix elements and a phenomenological relaxation time are also investigated. The results are compared with the experimental data.

Model study of the frequency-dependent dielectric properties of semiconductors

We present calculations of the frequency-dependent dielectric properties of semiconductors using the Penn model in the random-phase approximation, including collision effects via a phenomenological relaxation time $\ensuremath{\tau}$. Analytical expressions for ${\ensuremath{\epsilon}}_{1}(0,\ensuremath{\omega})$ (with and without collision effects) and for ${\ensuremath{\epsilon}}_{2}(0,\ensuremath{\omega})$ and $\mathrm{Re}\ensuremath{\sigma}(0)$ (including collision effects) have been obtained. The inclusion of collision effects leads to expressions which are valid in the entire energy range. However, they do not affect significantly the values of ${\ensuremath{\epsilon}}_{1}(0,\ensuremath{\omega})$ and ${\ensuremath{\epsilon}}_{2}(0,\ensuremath{\omega})$ except near the peak positions. Our calculations demonstrate that the peak heights in ${\ensuremath{\epsilon}}_{1}(0,\ensuremath{\omega})$, ${\ensuremath{\epsilon}}_{2}(0,\ensuremath{\omega})$, and $\mathrm{Im}[\ensuremath{-}{\ensuremath{\epsilon}}^{\ensuremath{-}1}(0,\ensuremath{\omega})]$ are sensitive to the value of $\ensuremath{\tau}$, while the peak positions are not.

Non-Markovian theory of resonant nonlinear-optical phenomena in the frequency domain

The resonant nonlinear-optical phenomenon in condensed matter due to two-frequency excitation is investigated by a first-principles theory without using the phenomenological relaxation-time description. A new generalized nonlinear susceptibility is introduced in order to describe the non-Markovian process in the condensed phase associated with the resonant four-photon parametric effect. It is shown that the present non-Markovian version of the theory of the resonant Rayleigh-type optical mixing (RROM) naturally includes the resonant coherent anti-Stokes Raman scattering (RCARS) as the memory effect of the reservoir. That is, the two phenomena PROM and RCARS are unified from the microscopic viewpoint. The general expressions for nonlinear susceptibility for RROM and RCARS are obtained by taking into consideration the frequency dependence of the transverse relaxation time ${T}_{2}$. These provide us the general guide for the study of several relaxation phenomena in condensed materials by means of resonant coherent nonlinear-optical methods.